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Math Help - find equations of tan lines parallel to line

  1. #1
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    find equations of tan lines parallel to line

    I am stuck on this problem:

    Find the equations of the tangent lines to the graph of the equation below that are parallel to the line given.

    f(x) = (x+1)/(x-1)
    Line : 2y+x=6
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  2. #2
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    Quote Originally Posted by sydewayzlocc View Post
    I am stuck on this problem:

    Find the equations of the tangent lines to the graph of the equation below that are parallel to the line given.

    f(x) = (x+1)/(x-1)
    Line : 2y+x=6
    1. find the slope, m , of the given line.

    2. set f'(x) = m and solve for values of x on the curve.

    3. evaluate the corresponding y-value for each x-value found in step 2 ... then use the point-slope form of a linear equation to write the tangent line equation.
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    i am still stuck on this problem, can anyone give me some help?
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  4. #4
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    Quote Originally Posted by sydewayzlocc View Post
    i am still stuck on this problem, can anyone give me some help?
    where are you stuck? ... show any work you have completed.
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  5. #5
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    Quote Originally Posted by sydewayzlocc View Post
    i am still stuck on this problem, can anyone give me some help?
    What is the slope of the line 2y+x=6?

    What is the derivative of the function f(x) = (x+1)/(x-1)?

    If you have been asked to do this problem then clearly you are expected to know how to do those. Please show what you have done on those.
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  6. #6
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    Post Re: find equations of tan lines parallel to line

    I'm stuck on the same problem, m = -1/2

    f '(x) = (-3)/(x-1)^2

    I set them equal and got x = 5
    y = -1/2x + 3/2
    but its wrong.
    Last edited by thurlow; February 18th 2014 at 02:08 PM.
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  7. #7
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    Re: find equations of tan lines parallel to line

    Your derivative is not correct.

    $f'(x) = -\dfrac{2}{(x-1)^2}$

    Hence, your numerator was incorrect. Using the correct derivative, you should be able to get the correct answers (there will be more than one).

    $-\dfrac{2}{(x-1)^2} = -\dfrac{1}{2}$

    $(x-1)^2 = 4$

    $x-1 = \pm 2$

    $x = 1 \pm 2$, so either $x = -1$ or $x = 3$.

    Then, $f(-1) = 0$ and $f(3) = 2$, so both lines should have slope $-\dfrac{1}{2}$, one should pass through the point $(-1,0)$ and the other through the point $(3,2)$.
    Thanks from thurlow
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  8. #8
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    Re: find equations of tan lines parallel to line

    Thanks so much!!! soo helpful. Yeah I added a 1 instead of multiplying by g '(x)
    Last edited by thurlow; February 18th 2014 at 02:36 PM.
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